=(x^2+y^2+1)(x^2+y^2+1)

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Solution for =(x^2+y^2+1)(x^2+y^2+1) equation: 


Simplifying
0 = (x2 + y2 + 1)(x2 + y2 + 1)

Reorder the terms:
0 = (1 + x2 + y2)(x2 + y2 + 1)

Reorder the terms:
0 = (1 + x2 + y2)(1 + x2 + y2)

Multiply (1 + x2 + y2) * (1 + x2 + y2)
0 = (1(1 + x2 + y2) + x2(1 + x2 + y2) + y2(1 + x2 + y2))
0 = ((1 * 1 + x2 * 1 + y2 * 1) + x2(1 + x2 + y2) + y2(1 + x2 + y2))
0 = ((1 + 1x2 + 1y2) + x2(1 + x2 + y2) + y2(1 + x2 + y2))
0 = (1 + 1x2 + 1y2 + (1 * x2 + x2 * x2 + y2 * x2) + y2(1 + x2 + y2))

Reorder the terms:
0 = (1 + 1x2 + 1y2 + (1x2 + x2y2 + x4) + y2(1 + x2 + y2))
0 = (1 + 1x2 + 1y2 + (1x2 + x2y2 + x4) + y2(1 + x2 + y2))
0 = (1 + 1x2 + 1y2 + 1x2 + x2y2 + x4 + (1 * y2 + x2 * y2 + y2 * y2))

Reorder the terms:
0 = (1 + 1x2 + 1y2 + 1x2 + x2y2 + x4 + (x2y2 + 1y2 + y4))
0 = (1 + 1x2 + 1y2 + 1x2 + x2y2 + x4 + (x2y2 + 1y2 + y4))

Reorder the terms:
0 = (1 + 1x2 + 1x2 + x2y2 + x2y2 + x4 + 1y2 + 1y2 + y4)

Combine like terms: 1x2 + 1x2 = 2x2
0 = (1 + 2x2 + x2y2 + x2y2 + x4 + 1y2 + 1y2 + y4)

Combine like terms: x2y2 + x2y2 = 2x2y2
0 = (1 + 2x2 + 2x2y2 + x4 + 1y2 + 1y2 + y4)

Combine like terms: 1y2 + 1y2 = 2y2
0 = (1 + 2x2 + 2x2y2 + x4 + 2y2 + y4)

Solving
0 = 1 + 2x2 + 2x2y2 + x4 + 2y2 + y4

Solving for variable 'x'.

Combine like terms: 0 + -1 = -1
-1 + -2x2 + -2x2y2 + -1x4 + -2y2 + -1y4 = 1 + 2x2 + 2x2y2 + x4 + 2y2 + y4 + -1 + -2x2 + -2x2y2 + -1x4 + -2y2 + -1y4

Reorder the terms:
-1 + -2x2 + -2x2y2 + -1x4 + -2y2 + -1y4 = 1 + -1 + 2x2 + -2x2 + 2x2y2 + -2x2y2 + x4 + -1x4 + 2y2 + -2y2 + y4 + -1y4

Combine like terms: 1 + -1 = 0
-1 + -2x2 + -2x2y2 + -1x4 + -2y2 + -1y4 = 0 + 2x2 + -2x2 + 2x2y2 + -2x2y2 + x4 + -1x4 + 2y2 + -2y2 + y4 + -1y4
-1 + -2x2 + -2x2y2 + -1x4 + -2y2 + -1y4 = 2x2 + -2x2 + 2x2y2 + -2x2y2 + x4 + -1x4 + 2y2 + -2y2 + y4 + -1y4

Combine like terms: 2x2 + -2x2 = 0
-1 + -2x2 + -2x2y2 + -1x4 + -2y2 + -1y4 = 0 + 2x2y2 + -2x2y2 + x4 + -1x4 + 2y2 + -2y2 + y4 + -1y4
-1 + -2x2 + -2x2y2 + -1x4 + -2y2 + -1y4 = 2x2y2 + -2x2y2 + x4 + -1x4 + 2y2 + -2y2 + y4 + -1y4

Combine like terms: 2x2y2 + -2x2y2 = 0
-1 + -2x2 + -2x2y2 + -1x4 + -2y2 + -1y4 = 0 + x4 + -1x4 + 2y2 + -2y2 + y4 + -1y4
-1 + -2x2 + -2x2y2 + -1x4 + -2y2 + -1y4 = x4 + -1x4 + 2y2 + -2y2 + y4 + -1y4

Combine like terms: x4 + -1x4 = 0
-1 + -2x2 + -2x2y2 + -1x4 + -2y2 + -1y4 = 0 + 2y2 + -2y2 + y4 + -1y4
-1 + -2x2 + -2x2y2 + -1x4 + -2y2 + -1y4 = 2y2 + -2y2 + y4 + -1y4

Combine like terms: 2y2 + -2y2 = 0
-1 + -2x2 + -2x2y2 + -1x4 + -2y2 + -1y4 = 0 + y4 + -1y4
-1 + -2x2 + -2x2y2 + -1x4 + -2y2 + -1y4 = y4 + -1y4

Combine like terms: y4 + -1y4 = 0
-1 + -2x2 + -2x2y2 + -1x4 + -2y2 + -1y4 = 0

Factor out the Greatest Common Factor (GCF), '-1'.
-1(1 + 2x2 + 2x2y2 + x4 + 2y2 + y4) = 0

Ignore the factor -1.

Subproblem 1
Set the factor '(1 + 2x2 + 2x2y2 + x4 + 2y2 + y4)' equal to zero and attempt to solve:

Simplifying
1 + 2x2 + 2x2y2 + x4 + 2y2 + y4 = 0

Solving
1 + 2x2 + 2x2y2 + x4 + 2y2 + y4 = 0

The solution to this equation could not be determined.

This subproblem is being ignored because a solution could not be determined.

The solution to this equation could not be determined.

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